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Wednesday, June 09, 2010

Lewisian realism and modal reduction

I’ve posted a draft of a new paper that, among other things, defends Lewis against the charge that he needs to employ primitive modality in order for his modal realism to be successful, thus undermining his claims to reduction. One thing I argue is that Lewis’s objectors fail to adequately distinguish two tasks: giving an account of what possibility is, and giving an account of the extent of possibility. The tasks are crucially different and, in my opinion, neither requires for its success the meeting of the other. In particular, an account of what possibility is can stay silent on the extent of what is possible.

So consider the Lycan/Shalkowski objection that Lewis needs a modal understanding of ‘world’ to ensure that there is the correct correspondence between worlds and possibilities, necessary for the material adequacy of Lewis’s account of possibility as truth at a world. Lycan says that Lewis needs ‘world’ to mean ‘possible world’ to rule out the inclusion of impossible worlds in Lewis’s ontology. Shalkowski says Lewis needs the notion of a world to be modal to ensure that the space of worlds is complete: that there are no worlds missing.

I think that’s wrong. What ensures that there are no impossible worlds is Lewis’s account of what possibility is. To be possible just is to be true at a world, so there’s simply no question of there being an impossible world for Lewis. Whatever worlds there happen to be, those worlds will all be possible and none of them impossible, because that’s just what possibility is. Similarly, there’s no question of there being a world missing – of there being a possible circumstance with no corresponding world. But what accomplishes this is not a modal understanding of ‘world’ but, again, Lewis’s account of what possibility is.

It just falls out from Lewis’s analysis that there’s no impossible world, and no possible circumstance unrepresented by a world. Now, here’s what doesn’t fall out from the analysis: that there’s no world with a round square as a part, or that there’s a world with a talking donkey as a part. But contra what Lycan and Shalkowski think, this doesn’t mean that Lewis’s analysis leaves it open that there are impossible worlds or not worlds enough for possibility. If it turns out that there’s a world containing round squares then this is not for it to turn out that there’s an impossible world, according to Lewis’s analysis – it’s for it to turn out that round squares are possible after all! Likewise, mutatis mutandis, if it turns out that there’s no world containing a talking donkey.

Now, Lycan and Shalkowski might complain that any analysis of modality that says that round squares are possible and talking donkeys impossible is not acceptable. Well maybe that’s right. But Lewis’s analysis of course doesn’t say this: it just doesn’t settle that round square are impossible or talking donkeys possible. But that’s fine: the account of what possibility is needn’t settle these claims about the extent of possibility. To demand that Lewis’s analysis settle these facts is to demand too much of analysis: it’s to confuse the two tasks that should be kept separate.

You might think that we need to be able to acquire warrant for thinking that there are no worlds with round squares and that there are worlds with talking donkeys if Lewis’s analysis is to be warranted in the first place. Well, again, that’s fine: Lewis has given us an argument for thinking that the space of worlds is like this. (Namely, that the posit that it is so is theoretically beneficial.) But it’s nothing about the meaning of ‘world’ or the nature of worlds that settles that the space of worlds is so, and nor need it be, since an account of what possibility is needn’t entail an account of the extent of possibility.

I think a similar thing is going on in Divers and Melia’s objection to Lewisian realism. Their argument is as follows. They assume that it’s possible for there to be alien natural properties, and so Lewis’s principle of recombination doesn’t give us a complete account of what worlds there are. Now, it seems that if there could be alien natural properties, there should be no finite bound on the number of possible alien natural properties out there. It seems ad hoc to say there are exactly 17, or a billion, alien natural properties in the multiverse; and so it seems that if we accept the possibility of alien properties in the first place, we should hold that for any finite natural number n, there are at least n alien properties to be found across the space of worlds. But once this is granted, argue Divers and Melia, there is no way to give in non-modal terms a complete account of what worlds there are. For we can’t just say that there are infinitely many alien natural properties spread across the worlds; or that for any finite n there is a world where n distinct alien natural properties are instantiated. Why not? Well, to satisfy those tenets there has to be, across the space of worlds, a denumerable sequence of alien natural properties P1, P2, . . ., Pn. Now, let S be the set of all the worlds that there are. S satisfies both those tenets, of course; but so does the set S* which is the subset of S containing all the members of S except those worlds where, say, P1 is instantiated. Because with P1 missing, there are still of course infinitely many alien properties left; so any tenet you laid down to tell you that there were infinitely many alien natural properties out there in the space of worlds won’t be able to discriminate between it being P1, P2, . . ., Pn that exist across the worlds or merely P2, . . ., Pn that exist. And so there is no tenet you can lay down that will completely yield all the worlds that there are. Unless, of course, we say something like ‘All the possible alien natural properties are instantiated somewhere across the space worlds’. And so the only way to completely say what worlds there are is to invoke primitive modality.

I think Divers and Melia’s argument that the Lewisian is not going to be able to give a complete account of the space of worlds in non-modal terms is pretty convincing. But unlike them, I see no reason to think this casts doubt on the reductive ambitions of the theory. Why should we demand that the Lewisian be able to give a complete non-modal account of what worlds there are? Given the Lewisian analysis, that’s to demand a non-modal account of the space of possibilities. But why should we demand this? To say what it is to be possible is one thing, to say what is possible another. Maybe no complete account of the space of possibility can be given: that should lead us only to epistemic humility, not to abandon a reductive account of what it is to be possible.

The paper goes into these issues in more detail, as well as making some methodological remarks about how to assess whether something can appropriately be included in a reductive basis. Comments on any of it would be welcome.

63 comments:

Thanks for posting this. It has convinced me that a paper I wrote arguing that MR fails as a reduction will need to be revised.

I have to think about this more, but briefly what I get from your paper is this idea: Lewis doesn't need to say a single thing about the extent ('plenitude') of worlds in order for his analysis to be true. However, the case is different from, say, an analysis of 'tallest' facts in terms of height facts, since we have no pre-existing judgements about other worlds (except perhaps that there aren't any).

The worry seems to be something like: there seems little reason believe anything about the worlds, except in order to make the 'right' modal claims come out true. But what are the 'right' modal claims?

Perhaps we can build a theory of the world using Lewisian ideology, but only by modeling it closely on our original theory of the world. But then what? What's to say we will be able to 'throw away the ladder' and make further judgements without using the old conceptual machinery? And how can we tell whether we have or not?

This is an interesting situation, and I agree it sheds light on the nature of reduction.

Hi, Jonathan Speke Laudly here, Possible just means it is true in some world? Why not just say it might turn out to be true in this world? Positing other worlds doesn't seem to me to make possibility any less ambiguous or arbitrary. Between saying it is possibly the case in this world or saying there is possibly a world where it is the case-or that the world where it is the case is possibly this world--I see little difference. Possible remains ambiguous. Possible as determined by what? By What happens? or by what has happened in the past in similar circumstances? Or is there no possibility despite appearances? Or is it possible despite appearances? Take your pick. Seems just a matter of personal preference--nothing necessary about it. I mean really, how do you settle such a question?: Is it possible that Joe will rob the liquor store when he says he is just going to buy some beer? No. Joe has no criminal record and is honest and trustworthy. Is it possible that Joe is a very good actor/lier and is actually a clever criminal though he seems honest? No. I have never known someone like Joe to be a closet criminal. OR-- Yes, it is possible. There have been such deceptively honest criminals, Joe might be one and we would never know it until he is convicted of a crime. Is possible determined by what actually happens? Joe remains seemingly honest all his life, no trouble with the law. So, it was not possible in Joe's case because he was never shown to be a criminal(never arrested etc). OR, No matter what actually happens Joe could still have been a criminal--just very good at hiding his true motives and his actions and erasing his tracks. Because some ostensibly honest people in fact aren't and only years after they die is their nefarious character revealed. OR, No matter that Joe is considered a criminal by some---I know he was framed and is an honest man---that he is a criminal is not possible. OR, In Joe's case the circumstances are similar to some who are found to be criminal in the past---but these circumstances do not apply to Joe. Take your pick. OR, statistically of people who appear honest 30% are criminal and so on this basis Joe is possibly criminal. OR, People who appear honest always have some dishonesty in thembut if the honesty predominates ,say 51%, then they are honest practically speaking, though you could say that they are possibly dishonest in the eyes of a few. Take your pick. Is it possible that I am a duck and am dictating this to the ghost of Marilyn Monroe? Yes. No. Take your pick. Imagination, it seems, is what is possible. And "conceptually possible"? Don't get me started.

Obviously I'm late to the party. I've got two sick kids and I'mfeeling under the weather myself, so I'll just fire off three quick comments.

(1) I agree in principle with your criticism of Divers & Melia's "Analytic Limit." Additionally, I've never understood why Lewis couldn't respond to Divers & Melia as follows: "The additional constraint on the class S of worlds is that every maximal (analogically) spatiotemporally connected whole is a member." It's true that, if you add this to Lewis's theory as an axiom, then there is an interpretation that satisfies the resulting theory, but uses only a subclass of all of the things that are *really* worlds. I believe Lewis had some things to say about metasemantics (e.g. in "Putnam's Paradox") that bear on this issue.

(2) Some of the theoretical benefits that Lewis claims for his view may require certain modal claims. For instance, Lewis claims to be able to say what it is in virtue of which *renate* and *cardiate* are distinct, despite being co-extensive: to wit, they have different members. But this requires the claim that it is possible that something be a cardiate but not a renate, or vice versa. Presumably, Lewis might add his proposed analysis of this claim as an extra theoretical posit; but that looks pretty seriously epicyclic, rather than an elegant way of systematizing and unifying phenomena. In general, then, it's a good idea for Lewis to try at least to give a simple way of expressing a lower bound on the extent of the possibilities.

(3) I've only skimmed your paper, but I notice that you characterize the advantage Lewis has over theories of possible worlds that take "possibly" as primitive as a matter of ideological parsimony. I think that Lewis cannot reasonably claim that he has a more ideologically parsimonious theory. Lewis eschews taking "possibly" as primitive. But he gains ideology by taking "property analogous to spatio-temporal connectedness" as primitive. (I'm at home right now, so I can't give a relevant page reference to Lewis (1986).)

On (1). I suppose D&M wouldn't like that, because it doesn't tell you *what* maximal wholes there are, and hence won't settle the extent of what's possible. Of course, I think there's no need for the analysis to settle that, and so I agree that's fine, but I take it that's why it won't do by their lights.

(2) I agree, of course, that Lewis owes us an account of what the space of possibilities is like. I just reject any constraints that says it has to follow simply from his account of what possibility *is*. But as I say in the paper, I do think he has to tell us something about what he takes the space of worlds to be like before we can make a judgment as to whether his theory is *warranted*. In particular, it *may* be the case that his theory is only warranted if it allows for an identification of properties with sets of individuals, and that this is only achieved if there's a world with a cordate that is not a renate, and vice-versa. But all he needs to do is say that there is such a world - he doesn't need it to follow from his analysis that there is such a world. Imo.

(3) Fair 'nuff. And I basically ignore that complication in the paper. But three points: (i) while I admit unease at comparing the different strengths of bits of ideology, I find it much more costly to take modality as primitive than I do to taking "property analogous to spatio-temp connectedness" as primitive. The former seems to me to carry much more weight. (ii) It's not obvious the Lewisian needs to take that as primitive anyway: can't we understand it in terms of 'spatio-temp connectendess' and similarity? (iii) Even though Lewis didn't like this, I'd be happy to just bite the bullet and claim it's really s-t connectedness that's unifying every world.

3.(ii) I'm not sure how the analysis in terms of s-t connectedness and similarity is supposed to go. You'll need to specify a respect of similarity; Lewis himself makes an attempt at Plurality, pp. 75-6, and criticizes this attempt in the following passage. At any rate, things don't look promising for anyone who shares Lewis's antecedent modal opinions to a great enough extent to endorse the possibility of infinitely many alien properties and relations.

3.(iii) Lewis worries that this will rule out by analytic fiat the possibility that a certain flavor of Newtonian physics might have been true. See Plurality, p. 75. I also worry that this tactic doesn't sit well with the kind of modal opinions which countenance infinitely many alien properties. On this point of view, there might have been objects that are massless, but have features that are mass-like in various ways. But then it's plausible to think that there might have been pairs of objects that aren't any distance apart from one another, but have a relation that is distance-like in various ways.

3.(i) This is, I think, what's really going on with Lewis. Lewis takes it as a significant mark in favor of his analysis that it needn't take "possibly" (or any other recognizably modal notion) as primitive. There's some reason to be especially suspicious of primitive modality (despite the familiarity and ubiquity of modality), and less suspicious of primitive analogous-to-spatio-temporal-relatedness. The question of what the special problem with modality is keeps me awake nights. This, it seems to me, is the rub.

I'm not that worried about ruling out the possibility of the certain type of Newtonianism. Taking s-t connectedness as being the worldmate relation also rules out the poss of island universes - is the former so much more objectionable than the latter?

But I guess I still don't see the need for an extra primitive even if we want to avoid this. What's wrong with the following line of thought? We have our notions of spatial and temporal connectedness. We notice they're similar: being spatially connected is somewhat like being temporally connected. So now let being s-t connected mean: connected by a relation that's similar to being spatio or temporally connected in the way that those are similar. Being spatio-temporally connected is just a way of being s-t connected: it's the way actual things are s-t connected. But now we have the notion of s-t connectedness, that can be our worldmate relation, and perhaps things in other worlds are s-t connected but not spatio-temporally connected. So that's not an analysis of how the analogous relation is built up out of spatio-temporal relations and similarity, but it's a story about how we could latch onto something like that concept, without adding a new primitive to our ideology.

On island universes: ruling out the possibility of island universes is less worrisome because there's a quick fix available a la Bricker: let the worlds be arbitrary sums of maximally (analogically) spatio-temporally connected wholes. To my mind, this does basically no damage to the basic Lewisian picture. Accommodating the possibility of Newtonianism, by contrast, appears to require new ideology. And, as I said above, the modal claims in question seem to me irresistable for someone who shares Lewis's antecedent modal opinions.

On latching on to the notion of s-t connectedness: Perhaps we mean something different by "primitive"? I mean a property or relation which is not to be analyzed in terms of a congeries of other properties or relations. Lewis claims to do without primitive modality, not in the sense that he shows how we can use other notions to latch on to "possibly", but in the sense that he proposes an analysis of "possibly" in terms of "part", "(analogically) spatio-temporally connected", etc. So I think that the fact that we can explain how we latch on to the notion of s-t connectedness does not speak to its primitivity in the relevant sense.

But Bricker needs a primitive notion of actuality, right? Much worse than taking 'analogous to s-t connectendess' as primitive!

What I was trying to get at with latching on to s-t connectedness was that we could take it as primitive, instead of spatiotemporal connectedness, with the latter taken as a determinant of the former determinable. So same number of primitives, it's just replacing one with another, with a story about how we can get to understand it.

I don't think Bricker needs primitive actuality to secure the possibility of island universes. He endorses primitive actuality, but for unrelated reasons IIRC; like you, I think endorsing primitive actuality would be a mistake for a Lewisian.

I completely missed your suggestion about s-t connectedness being a new primitive, and analyzing spatio-temporal connectedness in its terms. Sorry about that. It's a really interesting idea! I wonder whether someone who takes "possibly" as primitive can't pull off the same trick. All parties agree, we may assume, that s-t connectedness obtains as a matter of necessity between all and only worldmates. That is:

But the primitivist about "possibly" has a way of defining the (binary) worldmate relation:

(WM) Necessarily, x and y are worldmates iff x exists and y exists.

[NB: (WM) ignores sets, numbers, and other necessary existents.]

(S-TC) + (WM) opens the way to understanding s-t connectedness as coexistence. So, even if we assume that the analysis of spatio-temporal connectedness in terms of s-t connectedness can be made to fly, we're back to parity. (I assume no analysis of existence is in the offing for Lewis.)

At any rate, things have gotten sufficiently involved over the course of the discussion that I think we can agree that, barring a qualitative difference between primitive possibility and primitive s-t connectedness, Lewis's view is prima facie no more parsimonious than the modal primitivist's.

On Bricker: I thought they were related. Given Bricker's view on what worlds are, I am part of many worlds - so actuality can't be just me and my surroundings. And that's why we need primitive actuality: to mark out which of the many worlds that has me as a part is the actual one. No?

And while I'd love to agree on the main point, I don't think we do! I was thinking the Lewisian had a clear advantage over the primitivist, since they both need a connectedness primitive: for the Lewisian, it's s-t connectedness, and for the primitivist it's spatio-temporal connectedness. But then, the latter also needs modality.

That argument wouldn't be good if the primitivist could define spatio-temporal connectedness in terms of co-existence as you said. But I don't think that looks too hopeful: we ignored sets etc, but now it's time not to! In any case, even if all things are spatio-temporally connected, that seems like a substantial fact about the world - we'd still want to be able to state it without it being the trivial 'all things co-exist'.

Or were you just meaning to point out that Lewis didn't take the route I'm attributing here to the Lewisian?

* "Given Bricker's view on what worlds are, I am part of many worlds - so actuality can't be just me and my surroundings."

This does not seem to involve securing the possibility of island universes, so much as the non-actuality of them. In any case, I don't see why actuality can't continue to be explained as I and all my surroundings. It turns out then that I do not *actually* live in an island universe. In general, Bricker's line on actuality seems to me severable from his line on the possibility of island universes.

* "we ignored sets etc, but now it's time not to!"

Here's how the primitivist can ignore sets: they're necessary existents. S-t connectedness obtains only among contingent existents. I just left the qualification out to make the underlying idea shine through.

* "In any case, even if all things are spatio-temporally connected, that seems like a substantial fact about the world - we'd still want to be able to state it without it being the trivial 'all things co-exist'."

Agreed. But the co-existence analysis is of s-t connectedness, rather than spatio-temporal connectedness. I was proposing just to piggyback on your suggestion about how to analyze spatio-temporal connectedness. (I endorse a conditional: if the Lewis-Cameron analysis of spatio-temporal connectedness is adequate, so is the modal primitivist analysis.) So, it is of course a substantial fact that things are s-t connected in the particular way they are.

* "Or were you just meaning to point out that Lewis didn't take the route I'm attributing here to the Lewisian?"

Yep. Plus, that this route is not prima facie obvious. Give yourself some credit: it's really ingenious! And I guess I'm implicitly suggesting that the parsimony claim deserves scrutiny in your paper.

I think we're agreed on the substantive point. There's a (potential) way for the Lewisian to be as parsimonious w.r.t. s-t connectedness as the primitivist. Hence the Lewisian is at a potential advantage wrt parsimony in not having some primitive modal notion in addition. Agreed?

(I think you're right - I definitely need to bring this out in the paper. Thanks!)

The Bricker issue is obviously less important for my present purposes, but I still think the two points are related. Here's how I thought Bricker saw it, and what seems right to me. (I should re-read the Bricker, but . . . I'm lazy!) To deal with the possibility of island universes, Bricker says that every sum of Lewis worlds is a world. So consider two Lewis worlds: the one Lewis thinks is actual, @, and some non-actual world, w. Bricker thinks that @ and @+w are worlds. Both have me as a part. So there's more than world that I am a part of. Infinitely many, in fact. So the actual world isn't *my* world - there's no such thing. Hence we need a new actuality primitive to mark out one of the infinitely many worlds that has me as a part as the actual world. What goes wrong with this argument do you think?

Louis, what say you to the following argument? (This came out of discussion with Rich Woodward.)

While Lewis needs ideology enough to describe what there is, the primitivist needs ideology enough to describe both what there is and what could have been. After all, we need to give a complete description of reality - and for the primitivist, some of the facts to be described are facts about what could have been. (Whereas for Lewis, that's taken care of once you describe the facts about what there is.)

Assume that the Lewisian and the primitivist agree as to the extent of what is possible. Then if Lewis needs a primitive to describe some other worlds, the primitivist needs it to describe a possible alternative to the world. So if Lewis needs a new bit of ideology to describe those worlds where things are related by something other than spatio-temporal connectedness, the primitivist needs it to describe the possible way things might have been where things are so related.

Of course, the Lewisian and the primitivist don't really agree on the space of possibility. But then, Lewis is only going to need a new bit of ideology if it's needed to describe the peculiarly distinctive Lewisian commitments on what's possible: such as the impossibility of island universes. But that doesn't look to be the case.

So the primitivist needs all the ideology the Lewisian needs. The only question is whether the Lewisian needs all the ideology the primitivist needs. Answer: no, he doesn't! WDYT?

At any rate, I think the flaw in the argument is the claim that, if Lewis needs a new bit of ideology to describe the goings on in some range of worlds, then the primitivist does too. The problem is that the primitivist always has available a tool for analyzing the relevant notion that Lewis does not have: the notion can always be analyzed in modal terms.

I think this is what's going on in our little back-and-forth about s-t connectedness. Here's how things look to me:

This still looks like parity to me. Ordinarily, the Lewisian can adopt all of the modal analyses of derivative notions that the primitivist can. But not in the case of the primitivist's analysis of s-t connectedness in terms of possibility and existence, for the reason that s-t connectedness is supposed to be part of the Lewisian analysis of possibility.

So, it still seems to me as if the Lewisian has not yet been shown to have fewer ideological primitives.

But, I'm still not happy! I don't like the primitivist's analysis of s-t connectedness. You analysed it in terms of 'worldmates', and said the primitivist could analyse that basically as 'x and y are worldmates iff they are contingent and co-exist'. But how can the primitivist say this and allow for there being contingent entities not s-t related to anything, such as impure sets, or universals? Lewis can allow that with his story about 'existing from the standpoint of a world', but I don't know what the primitivist's story is.

I also don't like s-t connectedness being analysed in terms of being worldmates: even if it is in fact necessary that x and y are worldmates iff they are s-t connected, it doesn't seem like that is *what it is* to be s-t connected. But I admit to not doing much more than intuition thumping there!

So Bricker thinks that acceptance of primitive actuality is forced once you try to accommodate island universes, for pretty much the reasons Ross gave. If you analyze possibility in terms of sets, or sums, of worlds (or what have you) then you need to say something about how to define truth simpliciter. The only option, it seems, is to do so by saying its truth at the actualized set/sum of worlds. At least that's how I remember things.

Incidentally, no one seems to have noted that the actualist realist seems to have need of an extra primitive --- actualization, be that cashed out in terms of truth or obtaining or instantiation. And we need that to define truth simpliciter. At least that's one of the primitives that's often associated with the view. (I seem to remember that's one of the primitives JD lists for each species of actualist realism.)

I don't think Lewis is going to be able to define truth in terms of actuality, since he thinks there are truths that go 'way beyond what's actually true. Instead, he proposes, I think, to analyze actual truth in terms of truth aimpliciter + a quantifier restriction. Bricker can do the same, if he likes. (All of this modulo problems accommodating actuality and counterpart theory.) The primitivist will define actual truth (and "actual world") in terms of truth simpliciter.

In defense of the proposed primitivist analysis of s-t connectedness: Ross, I doubt I'll make you happy, but it seems to me there's three different ways for the primitivist to go:

(1) Set out on the Chisholm trail: Carve out exceptions for universals and sets in the analysis of s-t connectedness, using primitive set-membership and instantiation (which Lewis needs, by his own lights).

(2) Super-determinable! Suggest that s-t connectedness is a determinable of an even broader primitive notion, call it compresence, and then analyze s-t connectedness as a determinate of that determinable (and spatio-temporal connectedness as before).

(3) Deny the intuitions: say that impure sets and universals are s-t connected. On universals: Any Aristotelian theory is already committed to this: universals are "multiply located" in their instances. Even a Platonic theory could claim that universals are s-t connected "by courtesy" when their instances are. On impure sets: Consider {Plato} and {Kripke}, Plato and Kripke. Plato and Kripke are spatio-temporally connected: Plato temporally preceded Kripke. But, given the existential dependence of singletons on their members, it seems to me we should also say the same of {Plato} and {Kripke}.

I favor (3), since it answers to intuitions that I already have, and leaves the proposed analysis of s-t connectedness clean.

"I don't think Lewis is going to be able to define truth in terms of actuality, since he thinks there are truths that go 'way beyond what's actually true. Instead, he proposes, I think, to analyze actual truth in terms of truth aimpliciter + a quantifier restriction. Bricker can do the same, if he likes."

The cases are disanalogous.

In Lewis's case, actual truth gets defined in terms of a quantifier restriction, that's true, but (a) the domain of quantification is the worlds, and (b we can get a grip on the relevant restriction by means of the normal indexical account of actuality.

In Bricker's case, things are different because (a) the domain of quantification is the sets of worlds or the sums of worlds, which means (b) we can't get a grip on the relevant restriction by means of the normal indexical account of actuality. What's difficult to see is how to get a grip on it without recourse to a primitive notion of actuality.

I'm worried we've gotten side-tracked with the talk of s-t connectedness. I mean, here's the simple thought in favour of Lewis. We start off, we all need a primitive notion *being spatio-temporally related*. Lewis says, I'll use this to define 'world', and now I don't need 'possibly' - one up on the primitivist who needs 'possibly' as well. The primitivist says, but surely not every world is held together by the spatio-temporal relations that hold our world together? Lewis says: no, some are held together by spatio-temporal-relatedness*. But *if* I need to take that as primitive, so do you because you need to be able to describe the way the world *could* be held together as much as I need to describe how other worlds are held together.

So now, how does the primitivist answer this challenge? Is it open to them to define spatio-temporal-relatedness* but not Lewis? I can't see how that can be.

I think I was just muddying the waters unnecessarily with talk of determinates and determinables - this is the challenge to the primitivist.

And yeah, I agree with Rich. Without a primitive notion of actuality, Bricker has no way to say *how* to restrict the quantifier. Of course, he *could* restrict it in the same manner Lewis does - i.e. to the maximal mereological sum of spatio-temporally related things that has me as a part. He doesn't need primitive actuality to do *that*. But the problem is that given his views on worlds, that is totally ad hoc. *Why* restrict to that world when there are *many* worlds that have me as a part? What makes *it* the best candidate for actuality? Lewis has an answer; but without primitive actuality, Bricker doesn't. (Which is exactly why he wants it!)

I'm not sure when this debate happened, so I'm sorry if you've all lost interest by now.

I think that the primitivist does have an advantage over the Lewisian when it comes to analogical spactime connectedness, which uses Ross's answer to JD/JM's criticism. Essentially the problem is that some cosmoi may have alien spacetimes. Just as Lewisians don't need to say what the space of possibilities is, primitivists don't need to say what the space of actuality is like: it's us and all our worldmates, but if that includes properties or kinds of spacetime alien to our cosmos we'll never be able describe them. That's a shame, but knowledge is limited.

The problem is that the Lewisian may have to say something about the alien spacetimes, because it's part of their analysis of modality. Given what there is and how those things are related, the analysis should say what's possible, and that (probably) means saying which things are worldmates. That means saying what counts as analogically spacetime-related. The primitivist doesn't need to say this if they have an explicitly modal worldmate relation.

A primitive worldmate relation may be a piece of fairly heavy-duty ideology, but if appeals to s-t connectedness don't get us a non-primitive worldmate relation, maybe we need it.

But I do think it's worth seriously considering just using straightforward spatio-temporal connectedness. Since (for the Lewisian) other worlds can have the same universals but different laws, it's not obvious to me that a world with space and time couldn't be at least Newtonian enough to satisfy modal intuition. I don't know enough maths or physics to push this very far though.

Both Lewis and the primitivist can hold that there are facts about the space of possibility that are beyond our ken, or not expressible in English, and which certainly don't follow from the account of what possibility *is*. But I take it that we're talking about what ideology is needed, we're not talking about what English terms we need to be able to state the limited knowledge we have of reality - we're talking about how reality is, as a matter of fact, independently of what we know, structured. Think of the ideology that is needed as being what God would need to give a *complete* description of reality. So it's inappropriate, I think, to play the 'knowledge is limited' card: if there could be alien spacetimes, fundamental ideology must contain resources to describe such spacetimes (even if we do not, even cannot, grasp any primitive that will let us so describe them) - no matter whether modality is primtive.

(I do agree, though, that it's not obviously bad for the Lewisian to just stick with spatio-temporal connectedness. Who cares whether Newtonianism is impossible? Epistemic possibility is one thing, metaphysical possibility quite another! I, at least, have no intuitions about the possibility of alien spacetimes.)

I can agree that fundamental ideology needs to describe all the alien spacetimes there could be, and the primitivist needs an additional modal primitive, making his ideology less parsimonious.

If I have a remaining worry, it's that the Lewisian's analysis, combined with the fundamental facts about the pluriverse, may not entail all the facts about what is a worldmate of what.

I think the Lewisian analysis is only complete if there is a unique most natural [genus of which spacetime-relatedness is a species]. If there is such a genus, that can serve as the worldmate relation. If there isn't, the analysis leaves it open what is a worldmate of what. The primitivists' analysis won't though, because they can just read it off their primitive relation.

This said, if my worry is really something we should worry about, we might have a principled reason for saying a primitive worldmate relation would be ungraspable even if there was one.

Holy Schmokes! I take Independence Day off, and things get even more complicated!

Rich, Ross anticipated my response about a Bricker-friendly account of "actually": Bricker could just use Lewis's original account: the actual world is the minimal world containing me. Ross suggests this is ad hoc. A charge of ad hoc-ness is in effect a call for an argument favoring your view. The Lewisian has a one-size-fits-all argument: this is the most parsimonious sufficient theory. (NB: Bricker himself does not endorse this style of argument, and so goes for primitive actuality.)

Ross: I like this summary a lot:

"We start off, we all need a primitive notion *being spatio-temporally related*. Lewis says, I'll use this to define 'world', and now I don't need 'possibly' - one up on the primitivist who needs 'possibly' as well. The primitivist says, but surely not every world is held together by the spatio-temporal relations that hold our world together? Lewis says: no, some are held together by spatio-temporal-relatedness*. But *if* I need to take that as primitive, so do you because you need to be able to describe the way the world *could* be held together as much as I need to describe how other worlds are held together."

Two comments:(1) Insofar as the primitivist is inclined to endorse the existence of possible worlds at all, she can use "possibly" to define "possible world." (I have a paper on this, btw.)

(2) Having used "possibly" to analyze "world", the primitivist has an entirely natural thing to say about what holds worlds together: (possible) co-existence. So: no new primitive is necessary to answer the challenge.

To illustrate, consider the question, "In virtue of what do x and y coinhabit a world?"

Lewisian's answer: "In virtue of the fact that x and y are spatio-temporally* related."

Primitivist's answer: "In virtue of the fact that it is possible that x exist and y exist."

On the primitivist's line, all the ways a world could be held together are given by all the facts concerning which things might have co-existed.

Hey louis. The kind of semantic treatment of actual truth we're considering here provides us with a semantic guarantee that 'there are no island universes' is actually true, right? That just strikes me as way to strong. Even if you take yourself to know that there aren't actually any island universes, it's strange to think that even though such things are metaphysically possible, we've got semantic guarantee that this possibility isn't realized at the actual world.

To chip in on the discussion about spatiotemporal connectedness, the worry Ross and I were having wasn't so much about what the actualist will say about what holds the worlds together. It's rather that in order to describe what certain worlds represent the actualist will need the same primitives Lewis needs to tell us what holds his worlds together. At least, that's how i was thinking about the line of argument, and it's not clear to me how you're dealing with that argument.

Yeah, that's how I was thinking it too: it's nothing to do with how the primitivist defines 'possible world', or what they say about 'worldmate'. The thought is just that they need to say *what's going on* at those possible worlds where spacetime is alien - and it's hard to see how they're any better off than Lewis is when it comes to having the resources to say that.

That's because I wasn't dealing with that argument. Thanks for stating it in a way that could get through my thick skull! So, here's how I deal with it.

The problem is to characterize the possibilities in which individuals are stc* ("spatio-temporally* connected"), but not spatio-temporally connected. If the primitivist does it directly, like this:

(*) it is possible that there are x and y that are stc*, but not spatio-temporally connected

then she's got Lewis's new primitive, and the Lewisian has an inherent advantage in parsimony. Got it. (At last!)

I've been arguing that the primitivist could just say this:

(E) it is possible that there are x and y that exist only contingently, but are not spatio-temporally connected.

I have contended, in effect, that (E) is equivalent with (*), assuming Lewis is right about the extent of the possibilities. (If the Lewisian has an analysis of spatio-temporal connectedness let the primitivist deploy that analysis in (E).)

Alternatively, the primitivist could, instead, just appeal to the same old analogies as Lewis does, endorsing

(A) it is possible that there are x and y that are related in a way relevantly like spatio-temporal connectedness, but are not spatio-temporally connected.

(As before, if the Lewisian has an analysis of spatio-temporal connectedness let the primitivist deploy that analysis in (A).)

Now, (A) and (E) aren't couched in terms of what worlds represent, but they can be. (E), for instance, should be equivalent to the claim that there is a world which represents "there are x and y that exist only contingently, but are not spatio-temporally connected" as being true.

I see no further theoretical need which is not being addressed by the primitivist. But perhaps I still don't understand!

On actuality, you write: "it's strange to think that even though such things are metaphysically possible, we've got semantic guarantee that this possibility isn't realized at the actual world."

That's just what an actuality operator does. We've got a semantic guarantee that snow is white iff actually snow is white, but this is only a contingent truth.

I'll need to think about the first response, but a quick thought on the actuality stuff.

I wrote that it's strange to think that even though island universes are metaphysically possible, we've got semantic guarantee that this possibility isn't realized at the actual world, to which you responded:

"That's just what an actuality operator does. We've got a semantic guarantee that snow is white iff actually snow is white, but this is only a contingent truth."

Right, but my point was just that the semantics gives us a semantic guarantee that "there are no island universes" is actually true. The semantics *doesn't* give us a semantic guarantee that "snow is white" is actually true, and it doesn't give us a semantic guarantee that "there aren't any talking donkeys" is actually true, even though it gives us the truth of certain biconditionals, such as those you mention. But all we need to do is look at how actual truth gets defined and we'll see that "there are no island universes" is actually true. That's *very* different from what you normally get in the cases of the actuality operator.

What's central to your line is that we can maintain the equivalence of the following:

(*) it is possible that there are x and y that are stc*, but not spatio-temporally connected

(E) it is possible that there are x and y that exist onlycontingently, but are not spatio-temporally connected.

(I know there is stuff about (A) but I *think* the point to follow applies.)

The trouble I'm having is what you're going to say about:

(**) it is possible that there are x and y that are stc**, but not spatio-temporally or stc* connected

Roughly: the idea is that there are going to be *many* relations that are analogous to spatio-temporal connectedness, and your (E) doesn't discriminate between them. Basically, I'm wondering whether we can multiply the "alien" s/t-ish connections. If we can, we can't maintain the equivalence of (*) and (E).

Ok, so that probably pushes us to something like (A) and various variations of it. But then it seems like you're conceding we need the "analogous to a s/t connectness" primitive. But now I think I'm missing something important...

I don't just want to keep saying "I agree with Rich" but . . . I agree with Rich. The problem with the co-existence proposal is that it assumes the alien spacetimes are all of a kind, so that we can in effect define them via our notion of spatio-temporal connectedness and negation. But that doesn't seem to be the case.

(A) is fine, I think. But no help to the primitivist: that puts her back on parity with Lewis w.r.t. this issue, which is where Lewis wants her to be to make the dominance argument for ideological parsimony.

On actuality, I suspect we've just reached an impasse now. I think it's crazy to pick out one of the many worlds I am a part of and define it as the actual world when there is no relevant difference between it and the many other worlds I am a part of. And is it contingent that 'actual' gets it reference fixed like that? It's hard to see how it could be so, but if it's not, then every possible being can truly say that all actual things are spatio-temporally connected, despite there being the possibility of island universes? Odd!

Ross, since you agree with Rich I'll concentrate my remarks on his latest. Let's forget for the moment about Bricker and island universes. Richard's problem for the co-existence analysis of stc* concerns the alleged possibility given by

(**) it is possible that there are x and y that are stc**, but not spatio-temporally or stc* connected

If (**) is true, then the co-existence analysis of stc* won't work. But that should be no comfort to the Lewisian. Remember, it's the Lewisian who needs to appeal to stc* as what I will call her world-making relation. (A world-making relation is a relation R s.t. x is a world iff it is a maximally R-related sum: all of its parts are R-related, and none are R-related to anything not a part of x.) If (**) is true, then stc* is not a world-making relation, and any Lewisian theory that takes stc* as its world-making relation fails.

What I have offered in this series of comments is not so much a particular analytic proposal, as a dialectical strategy: the Lewisian needs to appeal to a new primitive, whether it be stc* or something else, for her world-making relation. But, given a choice of world-making relation R, the primitivist can respond as follows: "If your theory is not false, then it is impossible for there to be contingent entities which co-exist, but don't stand in R. But then I can use possible co-existence to analyze R. So, whatever world-maker R you choose, I can analyze something you take as primtive. So, either your theory is false, or we're at parity with respect to number of primitives."

Now, that still leaves open the question of how the primitivist should analyze (**). I say: if (**) is true, the primitivist should analyze it however the Lewisian proposes to. This preserves parity.

I don't think that's going to work, Louis. The point Rich is making, I think, is that Lewis won't have *a* world making relation. There will be as many world making relations as there are relations analogous to spatio-temporal connectedness. So *if* you need a primitive for each one, then Lewis needs a lot of primitives - but then, so does the primitivist to describe all these ways the world might have been.

(2) The inter-analyzability of the stc_n's bothers me no more or less than the inter-analyzability of `and', `or', 'not', the scheffer stroke, etc.; or of `possibly', `contingently', and `necessarily'.

(3) I was assuming that there were only finitely many stc_n's. If there are infinitely many, then the Lewisian will give an analysis of "world" that is infinitely disjunctive. What's sauce for the goose ...

Call it what you will, that wasn't my worry. I'm not worried by the interdefinability of 'and' and 'not' either. But I don't know anyone who thinks that by 'analysing' one in terms of the other, we don't need either in our primitive ideology! Likewise with necessity and possibility. We've got to take *one* as primitive, and the interdefinability just means we don't have to take *each* as primitive. But you want to take none of these notions as being part of your primitive ideology, defining them all out of modal notions and negation. My point was that I don't think having them all defined in terms of one another is going to let you do that.

Crud, I can see I haven't made myself clear! I didn't mean to suggest that the primitivist analyze all of the stc's (at once) in terms of one another. I agree with you that that would be, well, crazy. I meant to suggest that the primitivist take all but one of the stc's as primitive, and analyze the last one in terms of the others + existence + "possibly". So, it's just like the truth-functions, or the modal notions: the primitivist has to take all but one of the stc's as primitive; she doesn't have to take *each* as primitive, because one can be derivative; and, to a great extent, it's a matter of indifference exactly which ones she takes as primitive. In general, if a Lewisian theory proposes to take k of the world-making stc's as primitive, the primitivist can take (k-1) of them as primitive (with k=1 a special case). Add in the primitivist's primitive "possibly", and both the primitivist and the Lewisian ideologies have k primitives.

Okay, so if there are infinitely many, there really is parity before considering the case of modality, even by your own lights?And that looks plausible to me: why, if there could be more than one way of being s-t connected, would there be a finite bound on the number of possible ways to be so related?

Also, I think we've also got to think about numbers of kinds of primitives as well as number of primitives. If your primitivist has all but one of these as primitive, then they have as primitive a family of s-t relations. So does Lewis. But you've got modality as well, Lewis doesn't. The fact that Lewis has *one extra* primitive in the first family (assuming there's a finite number) . . . well, I think the case is strong for thinking that cost is massively outweighed by having a whole different kind of ideology in your fundamental ideology. But that really is to get in to the nitty gritty of intuition trading :-)

(At least I think we're talking on the same page again. For philosophy, that's progress!)

On the dispute about actuality, you wrote that an objectionable feature of the account is that "all we need to do is look at how actual truth gets defined and we'll see that "there are no island universes" is actually true." Given that "actually" is stipulated to restrict quantifiers, I don't see what's objectionable about that.

Consider a new operator, "unhorsily", which I hereby stipulate is such that

(H) `unhorsily P' is true iff the result of restricting all quantifiers in P to non-horses is true.

Then we have a semantic guarantee that `unhorsily, there are no horses' is true. To stretch usage a bit, we also have a semantic guarantee that `there are no horses' is unhorsily true. I have a hard time seeing how such results cause trouble for the stipulation.

Given the availability of a similar such stipulations for "actually", I don't see how this is objectionable.

Perhaps you think that there are some relatively pre-theoretic verities involving the actuality operator which aren't being respected. That's certainly Bricker's view.

"Perhaps you think that there are some relatively pre-theoretic verities involving the actuality operator which aren't being respected. That's certainly Bricker's view."

Yep: and one is that there no semantic guarantees that "Actually, there are no Fs" unless there is a semantic guarantee that "there are no Fs" is true.

Here's a quick argument I've not thought through to back this up.

Here is a plausible principle governing "Actually" (which seems to follow from the validity of "P iff Actually P"):

(A) If "Actually, p" is valid, then "p" is valid

And here is a plausible principle governing "Necessarily" (which is the semantic correlate of the necessitation rule):

(N) If "p" is valid, then "Necessarily, p" is valid

Put those two things together and you get (!):

(!) If "Actually, p" is valid, then "Necessarily, p" is valid.

The semantic setting you're considering forces us to reject (!): "Actually, there are no island universes" is valid, but "Necessarily, there are no island universes" is not. So either (A) or (N) must be wrong. But both strike me as immensely plausible principles.

As I say, I've not thought any of this through in detail, but it seems pretty compelling to me.

I don't think that can be exactly right. For Lewis, there's a semantic guarantee that "Actually, there are no objects with disconnected parts" is true, but no semantic guarantee that "There are no objects with disconnected parts" is true, since there are such objects.

Of course, that's because we're modalizing with one claim and describing the space of worlds as a whole with the other. But then, I take it Louis thinks something similar is going on with "Actually, There are no island universes" and "There are island universes".

But not *exactly* similar, since he does want to hold that there could be island universes, whereas Lewis doesn't want to hold that there could be individuals with disconnected parts, even though there are such things. That's why I focused on the example I gave: "Necessarily, it's actual that any two things are s-t connected, but there could be two things that are not s-t connected".

Now, I take it Louis isn't committed to the truth of this: he can say that it's true at those worlds with island universes that it's actual that there are island universes. But nonetheless, I take it that an inhabitant of one of those worlds still speaks truly if they say "Actually, any two things are s-t connected."

So Louis has to give up on one of two principle: that "Necessarily actually p" entails "Possibly p" or that "Possibly P" entails "Were p possible, I'd speak truly were I to say that p is true". Both those principles sound true to me.

Oi oi. we have to be careful here. What you do is switch from a case of ordinary modalizing (actually, there are no Fs) to a case of extraordinary modalizing (there are Fs). That's fine, but none of it threatens the principles I gave for just the same reasons that there is no threat to the T principle and what have you. But the argument I was giving wasn't treating 'there are no island universes' as an extraordinary claim, but an ordinary one.

I didn't think "There are Fs" was extraordinary modalizing. It doesn't appear to be modalizing at all! But I agree there are two readings of the claim: one where the quantifier is unrestricted, and one where it isn't. What I meant by "Louis thinks something similar is going on" was that I was conjecturing that he is happy for "Actually there are no island universes" to be semantically guaranteed, and takes the truth of "There are island universes" to not be in conflict precisely because there we've switched to the unrestricted quantifier, whereas 'actually' forces a restriction.

But once you say not just that there are (unrestrictedly) island universes, but that there *could be* island universes, things become trickier, was my thought.

Here's another way to put that. You hold the following claim: "there [are] no semantic guarantees that 'Actually, there are no Fs' unless there is a semantic guarantee that 'there are no Fs' is true".

I'm thinking that in the relevant sense, Louis thinks there is a semantic guarantee that there are no island universes. Speaking with the usual restriction on the quantifier to actualia, that's guaranteed to be true.

Of course, there are island universes. But now I've forced the context where I'm speaking unrestrictedly. But if I can still use that quantifier within the scope of actually, in this context there's no longer a semantic guarantee that there aren't actually any island universes.

So I think Louis can agree with your principle on either disambiguation: it only looks like he can't by shifting context.

I can see how Louis can hold onto principle (A). So if that's what you're pushing, I'll spot it. What I can't see is how he can hold onto (A) and (N) together. Maybe that's a stable position, but my point was simply that both strike me as pretty plausible constraints on the interpretation of actuality and necessity. So maybe what I should've said is that there can be semantic guarantees that actually p only if there are semantic guarantees that necessarily p. That's what (!) seems to say.

Right, good, I think we're in agreement now. Your claim that there can be a semantic guarantee that actually p only if there's a semantic guarantee that necessarily p is similar to my worry that every possible being can truly say that everything's s-t connected despite the possibility of things failing to be s-t connected. In each case, the worry is that possible circumstances shouldn't be ruled out as being actual by semantic fiat. Right?

There are apparent counter-examples to (!). For instance, let P be "snow is white iff actually: snow is white." Then `actually P' is valid, but `Necessarily P' is not.

One reaction is to suggest that (!) should be restricted to `actually'-free sentences. Another is to think that (!) (and, in particular, (N)) is just on the wrong track.

Another apparent counter-example: Let P be "I am here". (In case you don't think that Kaplan's treatment gives the correct semantics for `I' and `here', let me stipulate that I am using an artificial language for which that semantics is correct.) Then `Actually, I am here' is valid, but `Necessarily I am here' is not.

One reaction is to suggest that (!) should be restricted to indexical-free sentences. Another is to think that (!) (and, in particular, (N)) is just on the wrong track.

Back in the 60's, modal logicians working in QML got really worried about the rule of necessitation. In particular, they thought that sentences of the form `(Ax)Fx => Fa' were valid, but not necessitatable; to see the problem, just let F be "exists". If they are right, this is a third kind of counter-example to (!) (and, in particular, to (N)).

One reaction is just to change your notion of validity, e.g., moving to a free logic. Another reaction is to restrict the rule of necessitation. A final reaction is to abandon the rule of necessitation altogether. Either of the last two involves abandoning (N).

Finally, when it is stipulated that "actually" is a quantifier restrictor, then we should expect failures of (!), and of (A) in particular. For instance, that silly "unhorsily" operator I stipulated will yield counter-examples to the analogous claim:

($) `unhorsily P' is valid only if `necessarily P' is valid.

A counter-example is provided if we let P be `there are no horses.'

What is non-negotiable for an actuality operator? Three desiderata spring immediately to mind:

(1) The schema "P iff actually P" is valid.

(2) The schema "if actually P, then necessarily actually P" is valid.

(3) The operator can be used to model the natural language locutions which seem to require it, e.g., "Your yacht could have been longer."

For the record, it's not clear to me that Lewis's actuality operator delivers, especially on (1). But whatever problems it has on this score seem far removed from accommodating the possibility of island universes, or satisfying (!).

Whilst I agree that there are some delicacies with (A) and (N), I'm just not sure what to make of some of the cases.

The Kaplan thing is very subtle: we only get apparent failures of (N) when we hold character fixed over models, and we don't get failures when we don't. So if we're talking about *narrowly logical* consequence, and that's the sense of validity we're interested in, (N) is still ok. And then there are also issues to do with 1-necessity and the like. (Incidentally: we get apparent failures of (N) for non-indexical cases: "There are thinkers" is LD-valid but its necessitation is not.) I know people make a big deal of the Kaplan stuff, but the cases aren't obvious to me unless we make some very substantial assumptions.

And then there are issues to do with what's going on with names in QML which will have a bearing on the fate of (N).

Then there are also issues to do with (2) within Lewis's setting. Then there are also issues to do with what the philosophical significance of actuality operators and QML more generally. I know some people *think* in QML, but some --- Lewis? --- have thought it a thoroughly truncated, expressively inadequate medium that gets in the way of the real business of translating between natural language and the langauge counterpart theory.

So, yeah, the little argument I presented gets us into lots of issues that we're not in a position to answer. But let me back off to this: there is a prima facie in favour of the following:

If P is metaphysically contingent, then our semantics shouldn't entail that any possible individual can know that P is false at their own world.

The semantics you're backing forces us to reject that. That looks a bad-making feature of the semantics. Maybe it's negotiable --- maybe everything is --- but it's a cost nonetheless.

The prima facie virtue Rich identifies seems to be based on an argument like this:

(1) P is metaphysically contingent, so P is true at some worlds and false at some worlds.

(2) Let X be a world at which P is true, and Y be an individual at X.

(3) Y can know P is false at his world, which is X.

So P is false at X, which contradicts (2).

However, Louis's semantics for 'actually' doesn't lead to any contradictions, anymore than the semantics for 'unhorsily' does, although Rich and Ross are right that it has a peculiar feature which Bricker's primitive actuality is designed to counter. But it's hard spelling out exactly what this peculiar feature is.

We imagine an inhabitant of one of two island universes saying "there's only one universe" and think they must be wrong, but in fact they're not, because they are also part of a world which has only one universe, and that is the world they are talking about. The Anglophone inhabitants of island-universe worlds (and that includes us) just don't talk about the other islands.

The problem arises because in order to accommodate worlds containing island universes without introducing extra ideology we say that worlds are arbitrary sums of universes, and this means speakers will be parts of more that one world. Our intuitions about actuality work on the assumption we are parts of only one world, though. This is why it sounds fair enough in (3) when I said "his world, which is X".

One solution is to deny the possibility of island universes. Another is to say that when someone talks about actuality, or makes ordinary claims like "there are no talking donkeys", the quantifiers are restricted to the most natural world of which they are a part. This (presumably) will be the connected one. So although some worlds contain island universes with thinkers, these are not anybody's most natural world, which puts "there are no island universes", construed as an ordinary claim, roughly on a par with "there are no thinkers".

One can even say that the most natural worlds are the connected ones and the whole pluriverse, and charity determines that in ordinary contexts we restrict to the connected one, and in extraordinary contexts we restrict to the pluriverse.

The latter solution gives you the possibility of island universes, and while it does have odd results in the area under discussion, these are explained by our intuitions being based on the incorrect assumption that we're only parts of one world. Put this way, it sounds (to me) like a trade-off which is definitely negotiable.

Michael, I'm glad the suggestion I've offered the Lewisian doesn't turn out to entail a contradiction!

Rich, you offer an argument for rejecting the suggestion, based on this idea: "If P is metaphysically contingent, then our semantics shouldn't entail that any possible individual can know that P is false at their own world."

Is the P you have in mind is the sentence "there are island universes"? If so, the proposal does not run afoul of this claim. I can't know that "there are island universes" (as uttered by me here and now?) is false at my own world, because, as Michael notes, no world is uniquely my own. I can know that it is false at the minimal world containing me (if, that is, I can know the truth of the Lewisian theory under discussion), but that doesn't seem to me to be a problem.

- Louis

P.S. I'd like to ask you about your remarks on the Kaplan stuff when we see one another in Berlin.

I can't speak for Louis, but on my suggestion it would work like this:

Since I'm part of many worlds, "my world" has no unique satisfier, so saying "there are no other island universes in my world" has a failed definite description. The quantifier doesn't get restricted because the claim is an extraordinary claim about worlds, not an ordinary one about universes.

But when I say "there are no island universes" or "actually there are no island universes" the quanitifers are restricted to my most natural world, in the former case by its being an ordinary claim, and in the latter by the actually operator.

Both these are true, because my most natural world is the minimal one. This secures p iff actually p.

Hi Michael. I don't get how your thing is meant to work. You want to say that there are various candidate semantic values for "my world". And you want to say that the most natural candidate is the minimal world. But then why doesn't naturalness break the tie and force the reference of "my world" to the minimal world? Naturalness is there, in part, to break ties when other things are equal. And by your own lights it breaks ties in the normal case of "there are no island universes".

Remember how I had doubts that the Lewisian (either in Lewis's original theory, or in the souped-up version I've been suggesting) could endorse the validity of

(*) P iff actually P

? This is (part of) why. The Lewisian can say that every instance of (*) is true-at-@, but, I think, can't say that it is true simpliciter (with quantifiers in P on the LHS wide open). To see that this is not peculiar to the suggestion I offered, let P be "there are no talking donkeys". (There's some discussion between you and Ross on a related point a little farther up.)

So: *I* think that (*) is non-negotiable. But the Lewisian, I think, has to say something a little subtler. Maybe Michael's suggestion is a start. Anyway, all this is quite independent of the dispute over the possibility of island universes.

I was thinking there are no candidate values for "my world", because no world is uniquely mine, and a world would have to be my only world to be a candidate. In the case of "there are no island universes/talking donkeys" there are several candidates for the domain of quantification, and naturalness selects the most natural world of which I'm a part.

Alternatively, we could view "my world" as an incomplete definite descripiton referring to the most salient of my worlds, which could plausibly be the minimal one, perhaps because of its naturalness. If we do look at it this way though, there's no guarantee that "Y's world" will refer to a world X just because Y is part of X. The problem in the argument I set out is still with (3).

Either way "my world" is understood, thinkers will only be able to know that there are no island universes at their most natural world. Island universes with thinkers in are possible because of worlds which are nobody's most natural one.